This is an introduction to the lectures and the tutorials. We will study different topics, differential geometric topic using analysis for the lectures and topological topics with numerical experiments for the tutorials. A survey for the knot energies will also be given.
Creator:
O'Hara, Jun (Chiba University)
Created:
2019-06-17
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
We begin with the generalization of electrostatic energy of charged knots, where we come across the difficulty of divergent integrals. Two kinds of regularization will be introduced, Hadamard regularization and the regularization via analytic continuation, both from the theory of generalized functions.
Creator:
O'Hara, Jun (Chiba University)
Created:
2019-06-18
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
We will see that Hadamard regularization and the regularization via analytic continuation give essentially the same information. This part is rather technical, although it will save complicated computation afterward.
Creator:
O'Hara, Jun (Chiba University)
Created:
2019-06-20
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
We apply the regularization via analytic continuation to generalized Riesz energies of submanifolds in Euclidean spaces to obtain Brylinski's beta function, which is a meromorphic function with simple poles. We study geometric information that can be derived from Brylinski's beta function.
Creator:
O'Hara, Jun (Chiba University)
Created:
2019-06-21
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
A method to construct M\"obius invariant weighted inner products on the tangent spaces of the knot space by using M\"obius invariant knot energies will be introduced. It gives M\"obius invariant gradients of such energies."
Creator:
O'Hara, Jun (Chiba University)
Created:
2019-06-25
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
PhotoAcoustic Tomography (PAT) has become established as a significant imaging modality allowing the qualitative imaging in 3D of absorbed optical energy in the visible and near-infrared range, with high resolution, by exploiting the conversion of optical to acoustic energy and the discontinuity preserving propagation of ultrasound under the ass...
Creator:
Arridge, Simon (University College London)
Created:
2019-04-29
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
A prominent concern, in the age of machine learning and data analysis, is that left to their own devices, algorithms will propagate - even amplify - existing biases. Common definitions of fairness are group-based, typically requiring that a given statistic be equal across a few demographic groups, socially identified as deserving protection. Suc...
Creator:
Reingold, Omer (Stanford University)
Created:
2019-06-19
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
We present a novel active learning algorithm for community detection on networks. Our proposed algorithm uses a Maximal Expected Model Change (MEMC) criterion for querying network nodes label assignments. MEMC detects nodes that maximally change the community assignment likelihood model following a query. Our work is inspired by detection in the...
Creator:
Kushnir, Dan (Nokia Bell Labs)
Created:
2020-11-06
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
In this work we discuss the problem of active learning. We present an approach 2 that is based on A-optimal experimental design of ill-posed problems and show 3 how one can optimally label a data set by partially probing it, and use it to train 4 a deep network. We present two approaches that make different assumptions on 5 the data set. The fir...
Creator:
Haber, Eldad (University of British Columbia)
Created:
2020-11-11
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
The Metropolis Algorithm is an extremely useful and popular method of approximately sampling from complicated probability distributions. "Adaptive" versions automatically modify the algorithm while it runs, to improve its performance on the fly, but at the risk of destroying the Markov chain properties necessary for the algorithm to be valid. I...
Creator:
Rosenthal, Jeffrey (University of Toronto)
Created:
2021-03-23
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
In this talk I will introduce the back-and-forth method, a new algorithm to efficiently solve the optimal transportation problem for a general class of strictly convex transportation costs. Given two probability measures supported on a discrete grid with n points, the method computes the optimal map in O(n log(n)) operations using O(n) storage s...
Creator:
Jacobs, Matthew (University of California, Los Angeles)
Created:
2020-11-11
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Data classification, where the goal is to divide data into predefined classes, is a fundamental problem in machine learning with many applications, including the classification of 3D sensory data. In this paper, we present a data classification method which can be applied to both semi-supervised and unsupervised learning tasks. The algorithm ...
Creator:
Rapinchuk, Ekaterina (Michigan State University)
Created:
2020-09-14
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Knots are fascinating objects: featured in low dimensional topology, while gaining a strong visibility in biology, physics, material science and more. A multitude of knot invariants have been introduced to characterize and classify knots. The computational complexity often turns out to be exponential in the number of crossings of a knot, which i...
Creator:
Sazdanovic, Radmila (North Carolina State University)
Created:
2019-06-27
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Fitting a model to a collection of observations is one of the quintessential questions in statistics. The standard assumption is that the data was generated by a model of a given type (e.g., a mixture model). This simplifying assumption is at best only approximately valid, as real datasets are typically exposed to some source of contamination. H...
Creator:
Diakonikolas, Ilias (University of Southern California)
Created:
2019-06-18
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Image compression, as a subset of image processing, intersects many areas of applied mathematics. In this talk, I will describe and compare the "classic" view of image compression, such as the JPEG algorithm and it's variants, against the "new kid on the block", namely compression using neural networks (NN). I will survey the relative merits of ...
Creator:
Finlay, Chris (Deep Render)
Created:
2020-10-23
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
In many scientific areas, a deterministic model (e.g., a differential equation) is equipped with parameters. In practice, these parameters might be uncertain or noisy, and so an honest model should provide a statistical description of the quantity of interest. Underlying this computational question is a fundamental one - If two "similar" functio...
Creator:
Sagiv, Amir (Columbia University)
Created:
2021-01-26
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
We study the problem of prediction of binary sequences with expert advice in the online setting, which is a classic example of online machine learning. We interpret the binary sequence as the price history of a stock, and view the predictor as an investor, which converts the problem into a stock prediction problem. In this framework, an investor...
Creator:
Drenska, Nadejda (University of Minnesota, Twin Cities)
Created:
2020-11-10
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
The starting point for this work is the following observation: there exists a phase field approximation of the Willmore flow that seems to prevent, at least numerically, the appearance of self-intersections. Recall that the phase field approximation method allows to approximate the singular energy of singular functions by smooth energies of smoo...
Creator:
Masnou, Simon (Université Claude-Bernard
Created:
2020-09-14
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
In porous media, the motion of charges at the fluid/solid interfaces induces a coupling between seismic and electromagnetic waves. This phenomenon, known as the electro-kinetic effect is at the heart of electroseismic imaging, a technique used in oil prospection to image sedimentary layers of porous media. It combines the high sensitivity to mat...
Creator:
Bonnetier, Eric (Université Grenoble-Alpes)
Created:
2019-05-03
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
The simplest and most widely applied method for guaranteeing differential privacy is to add instance-independent noise to a statistic of interest that is scaled to its global sensitivity. However, global sensitivity is a worst-case notion that is often too conservative for realized dataset instances. We provide methods for scaling noise in an in...
Creator:
Steinke, Thomas (IBM)
Created:
2019-06-20
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
